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Computer Graphics docs

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Course
COMPUTER GRAPHICS

Institution
BVRIT

This document contains: TRANSFORMATIONS, Two-dimensional transformations, TRANSLATION, SCALING, ROTATION, Three-dimensional transformations, Concatenation, Vector Generation, DDA Algorithm, Bresenham’s Algoritm, Clipping, Line Clipping, Cohen Sutherland Line Clipping Algorithm, Sutherland-Hodgem...

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Uploaded on May 25, 2022
Number of pages 22
Written in 2020/2021
Type Class notes
Professor(s) Sirisha
Contains All classes

transformations
translation
scaling
rotation
concatenation
vector generation
dda algorithm
line clipping
clippin
two dimensional transformations
three dimensional transformations
bresenham’s algoritm

Institution
BVRIT
Course
COMPUTER GRAPHICS

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CADCAM

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1. Class notes - Input and output devices
2. Class notes - Cadcam intro
3. Class notes - Computer graphics
4. Class notes - Computer graphics docs
5. Class notes - Geometric modeling
6. Class notes - Curves(cad)
7. Class notes - Surface representation(cad)
8. Class notes - Numerical control
9. Class notes - Manual part programming
10. Class notes - Apt(automatically programmed tool)
11. Class notes - Group technology(cadcam)
12. Class notes - Computer-aided quality control
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UNIT II

COMPUTER GRAPHICS

TRANSFORMATIONS

Many of the editing features involve transformations of the graphics
elements or cells composed of elements or even the entire model. In this section we
discuss the mathematics of these transformations. Two-dimensional transformations
are considered first to illustrate concepts. Then we deal with three dimensions.

Two-dimensional transformations
To locate a point in a two-axis cartesian system, the x and y coordinates are
specified. These coordinates can be treated together as a 1x1 matrix: (x,y). For
example, the matrix (2, 5) would be interpreted to be a point which is 2 units from
the origin in the x-direction and 5 units from the origin in the y-direction.

This method of representation can be conveniently extended to define a line
as a 2 x 2 matrix by giving the x and y coordinates of the two end points of the line.
The notation would be

x 1 y1 
L=
x y 
 2 2

Using the rules of matrix algebra, a point or line (or other geometric element
represented in matrix notation) can be operated on by a transformation matrix to
yield a new element.

There are several common transformations used in computer graphics. We
will discuss three transformations: translation, scaling, and rotation.

TRANSLATION. Translation involves moving the element from one
location to another. In the case of a point, the operation would be

x' =x + m, y' = y + n

where x', y' = coordinates of the translated point

x, y = coordinates of the original point

m, n = movements in the x and y directions, respectively

In matrix notation this can be represented as

,(x', y') = (x, y) + T

, where

T = (m,n), the translation matrix

Any geometric element can be translated in space by applying Eq. to each
point that defines the element. For a line, the transformation matrix would be applied
to its two end points.

SCALING. Scaling of an element is used to enlarge it or reduce its size. The
scaling need not necessarily be done equally in the x and y directions. For example, a
circle could be transformed into an ellipse by using unequal x and y scaling factors.

The points of an element can be scaled by the scaling matrix as follows:

(x' ,y') = (x,y)S

where

m 0 the scaling matrix
s 
0 n

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